x^2-x+22=7x+7

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Solution for x^2-x+22=7x+7 equation: 


Simplifying
x2 + -1x + 22 = 7x + 7

Reorder the terms:
22 + -1x + x2 = 7x + 7

Reorder the terms:
22 + -1x + x2 = 7 + 7x

Solving
22 + -1x + x2 = 7 + 7x

Solving for variable 'x'.

Reorder the terms:
22 + -7 + -1x + -7x + x2 = 7 + 7x + -7 + -7x

Combine like terms: 22 + -7 = 15
15 + -1x + -7x + x2 = 7 + 7x + -7 + -7x

Combine like terms: -1x + -7x = -8x
15 + -8x + x2 = 7 + 7x + -7 + -7x

Reorder the terms:
15 + -8x + x2 = 7 + -7 + 7x + -7x

Combine like terms: 7 + -7 = 0
15 + -8x + x2 = 0 + 7x + -7x
15 + -8x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
15 + -8x + x2 = 0

Factor a trinomial.
(3 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {3, 5}

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